%0 Journal Article %T Semi-analytical solution for a system of competition with production a toxin in a chemostat %A Alderremy, Aisha Abdullah %A Chamekh, Mourad %A Jeday, Fadhel %J Journal of Mathematics and Computer Science %D 2020 %V 20 %N 2 %@ ISSN 2008-949X %F Alderremy2020 %X The resolution of a system for modeling the competition between opponents in a chemostat when one of these can produce a toxin has been studied. We propose a novel method to overcome the analytical difficulties of standard mathematical methods. The method is based on the variational iteration method and combined with the Gauss-Seidel technique for increasing the convergence rate. Numerical examples are considered to demonstrate the practicality and improve the convergence of the proposed method. %9 journal article %R 10.22436/jmcs.020.02.07 %U http://dx.doi.org/10.22436/jmcs.020.02.07 %P 155--160